class Solution:
    def minDistance(self, word1: str, word2: str) -> int:
        m, n = len(word1), len(word2)
        # 有一个字符串为空串
        if n * m == 0:
            return n + m 
        
        dp = [[0] * (n + 1) for _ in range(m + 1)]

        # 边界状态初始化
        for i in range(m + 1):
            dp[i][0] = i
        for j in range(n + 1):
            dp[0][j] = j
        
        # 计算所有 DP 值
        for i in range(1, m + 1):
            for j in range(1, n + 1):
                left = dp[i - 1][j] + 1
                down = dp[i][j - 1] + 1
                left_down = dp[i - 1][j - 1]
                if word1[i - 1] != word2[j - 1]:
                    left_down += 1
                dp[i][j] = min(left, down, left_down)
        
        return dp[m][n]